Question

3. Let S be a function such that – r2 <f(r)<?? for the interval [-10,10). Does the squeeze theorem apply when finding lim +1} (x)? If so find the limit. If not, for what a value is the squeeze theorem viable? (8 points) 4. Let f(x) = 3.22 +5%. Using the limit definition of derivative prove that f'(x) = 6.2 +5. Only prove this using the limit definition; any other method will not count. (8 points).

Answer 1

-x² <fox, exe lim x2 = 1 + lim -Y? = -1 X-2 Squeeze theorem limx2 lim Ex² = X-Yo is applicable when x --- x - -) 2x9220=), squeeze theorem is applicable atxo f(x)= 3x754) f'(x)= limf(x+h)-f(x) lime - f(x) lim 3(x+62 +5k+h)-22-57 -h70 Elim ho از همه جا diem 3(x+m² -x] +5 h - lim 3[v+h+2x4-2355 hno 3h (h+2x) 5h 3h*2*5 h 6x +5 5. f(x)= 3x?+5 f'(x)- 6x +5 (We've found) f(3) = 23 f(3) = 42 Equation of tangent (4-42) = 23(x-3) => 234-4-2720 6. average rate of change between x=+ &n=2 22-(-2) f(2)=-4-1) 225 3